How to avoid desaturation when using glossy material
Compositor &amp; Render Layers.  Enable Glossy direct.  Isolate/Transform gloss/specular with color ramp.  [Alpha Over] node to combine images.  The image below isolates some specular/gloss.  





When you use the mix shader you have an option to specify the mix .. labelled [fac].  Change the setting to suit your taste.
Consider rendering the image once as diffuse and once with specular.  Use the compositor to threshold with color ramp and choose the best color. PR or NPR? Suit to your tastes. More work.
Use more elaborate nodes in the materials to change the effect of specular. More work.